Random Walks in the Quarter-Plane
Subtitle: Algebraic Methods, Boundary Value Problems and Applications
By: by Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
Contributors: Iasnogorodski, Roudolf; Malyshev, Vadim
Series: Applications of Mathematics Stochastic Modelling and Applied Probability -- 40; Applications of Mathematics Stochastic Modelling and Applied Probability -- 40.
Publisher: Springer Berlin Heidelberg
Published: 1999
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 160
ISBN-13: 9783642642173; 9783642600012
Subjects: Mathematics; Distribution (Probability theory); Global analysis (Mathematics); Mathematical statistics
Description: This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.
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Table of contents: title: Introduction and History; title: Probabilistic Background; title: Foundations of the Analytic Approach; title: Analytic Continuation of the Unknown Functions in the Genus 1 case; title: The Case of a Finite Group; title: Solution in the Case of an Arbitrary Group; title: The genus 0 case; title: Asymptotics; title: References.